[Homer-users] Question on hmrMotionCorrectWavelet.

[Sabrina Brigadoi]

Dear Taka,

the wavelet motion correction algorithm implemented in Homer2 is not
exactly the method explained in Molavi and Dumont's paper. It is inspired
by that work and most of the code is very similar, though using a different
wavelet toolbox. The main difference is the threshold used. Molavi uses
alpha, a probability threshold for the coefficient distribution. The IQR
metric used in Homer2 is instead related to the interquartile range of the
wavelet coefficients distribution. All coefficients above Q3 + IQR times
the interquartile range (iqr) or below Q1 - IQR times the interquartile
range (iqr) are set to 0 and considered outliers of the distribution.
Usually, for outlier detection, IQR = 1.5. But for the nirs data, IQR can
be a tuning parameter, and can be set by the user depending on the amount
of noise present in the data. Using IQR = 1.5 is usually more conservative
than using the alpha=0.1 by Molavi. Reducing IQR, more coefficients are set
to 0 and more noise is removed. IQR should be set by the user depending on
the data, it cannot be fixed.

I am not sure about the relation between Molavi's alpha and iqr used in
Homer2, but looking at the maths it seems that the interquartile range of a
normal distribution is defined as: 2 Φ−1(0.75)σ  where  Φ−1 is the quantile
function and in Homer2 therefore, I think that the threshold can be defined
as Φ−1(0.75) + IQR*2 Φ−1(0.75)σ where IQR is the user set variable for the
upper threshold and Φ−1(0.25) - IQR*2 Φ−1(0.75)σ  for the lower threshold.

I hope this is useful and makes sense.

Sabrina

--
Sabrina Brigadoi, PhD
Research Associate
Biomedical Optics Research Laboratory
Malet Place Engineering Building, Rm 3.18
University College London
Gower Street
London WC1E 6BT


2015-03-20 10:39 GMT+00:00 Takayuki Nozawa <nozawa at idac.tohoku.ac.jp>:

> Dear Homer2 experts,
>
> Thank you for sharing the great toolbox.
> I have a question about the Wavelet motion correction function,
> hmrMotionCorrectWavelet.m and WaveletAnalysis.m.
>
> Comparing the code with the original paper
> Molavi et al.,Physiol Meas, 33, 259-270 (2012),
> I deduced that the interquartile multi factor iqr would basically
> correspond to the outlier threshold alpha in Molavi2012 by
> 2 * (1 - pnorm(0.75*iqr)) = alpha,
> with pnorm(q) being the normal cumulative distribution function.
> Am i correct on this?
>
> Confirmation or correction would be much appreciated!
>
> Best,
> Taka
>
> --
> Takayuki Nozawa
> Assistant Professor, Smart Ageing International Research Center
> Institute of Development, Aging and Cancer (IDAC), Tohoku University
> nozawa at idac.tohoku.ac.jp
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